Quadratic equations over p-adic fields and their applications in statistical mechanics

Saburov, Mansoor and Ahmad, Mohd Ali Khameini (2015) Quadratic equations over p-adic fields and their applications in statistical mechanics. ScienceAsia, 41 (3). pp. 209-215. ISSN 1513-1874

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Abstract

The p-adic models of statistical mechanics require the investigation of the roots of polynomial equations over p-adic fields in order to construct p-adic Gibbs measures. The most frequently asked question is that whether a root of a polynomial equation belongs to the classic domains not. This question was open even for a quadratic equation. In this paper, by using the Newton polygon, we provide solvability criteria for quadratic equations over the domains mentioned above for all odd primes p. We also study the number of roots of quadratic equations over all domains given above. This study allows us to present a local description of roots of quadratic equations over p-adic fields whenever p > 2.

Item Type:	Article (Journal)
Additional Information:	6769/45055
Uncontrolled Keywords:	solvability criterion, number of roots, Potts model, p-adic Gibbs measure, Newton polygon
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Dr Mansoor Saburov
Date Deposited:	12 Oct 2015 09:55
Last Modified:	16 Aug 2017 12:27
URI:	http://irep.iium.edu.my/id/eprint/45055

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